Flow structure and transport mechanism in lower half heated upper half cooled enclosures in laminar flow regime

This paper presents an investigation on the transport mechanism in autoclave/thermosyphon type enclosures. Without a baffle to separate the lower- from the upper-half, the flow structure and the transport mechanisms are the same in rectangular and cylindrical enclosures. Thus, the efficiency of the fluid exchange and heat transfer between the enclosure’s two halves due to wall-layers feeding structure ensures that the center cores have almost uniform temperature. However, when a baffle separates the two halves, the wall layers’ interactions are eliminated and two temperature zones are established.     

Flows in a lower half heated upper half cooled cylindrical model reactor loaded with porous media

This paper presents an experimental and numerical investigation on the natural convection flow in a cylindrical model hydrothermal reactor. The flow is visualized non-intrusively and simulated with a conjugate computational model. Results show that the flow structure consists of wall layers and core flows. In the lower half, the flows are steady due to the porous media. The three-dimensional unsteady upper core flow is driven by the streams originated from the wall layer collision. The thermal condition in the upper half core region is mainly determined by the total heat flow rate specified on the lower sidewall; while the variations of porous media parameters, in the normal range for hydrothermal crystal growth process, have minor effects.     

Transient natural convection in a rectangular enclosure with one heated side wall

This paper describes a numerical and theoretical study of the transient natural convection heating of a two-dimensional rectangular enclosure filled with fluid. The heating is applied suddenly along one of the side walls, while the remaining three walls are maintained insulated. It is shown that the process has two distinct phases, an early period dominated by conduction and a late period dominated by convection. The scaling laws for the heat transfer rate and the effectiveness (energy storage fraction) are determined based on scale analysis. These theoretical results are confirmed by numerical experiments conducted in the domain Ra = 10³−10⁶, Pr = 7, A = 1, where Ra is the Rayleigh number based on height and initial temperature difference, Pr is the Prandtl number, and A is the height/length ratio of the enclosure. Correlations for heat transfer rate and effectiveness are constructed by comparing the theoretical scaling laws with the numerical results.     

Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects

The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour coefficients around the density maximum is studied numerically. The right vertical wall has constant temperature θ_c, while left vertical wall is partially heated θ_h, with θ_h > θ_c. The concentration in right wall is maintained higher than left wall (C_c < C_h) for case I, and concentration is lower in right wall than left wall (C_h > C_c) for case II. The remaining left vertical wall and the two horizontal walls are considered adiabatic. Water is considered as the working fluid. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. The effect of the various parameters (thermal Rayleigh number, center of the heating location, density inversion parameter, Buoyancy ratio number, Schmidt number, and Soret and Dufour coefficients) on the flow pattern and heat and mass transfer has been depicted. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.     

Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.     

Conjugate conduction-natural convection in an enclosure with time-periodic sidewall temperature and inclination

The unsteady conjugate conduction-natural convection in enclosure is of great theoretical significance and is widely encountered in engineering applications in the areas of fluid dynamics and heat transfer. However, there are relatively few efforts to investigate the unsteady flow physics and heat transfer characteristics in the inclined enclosure of finite thickness walls. In the present work, this problem is numerically investigated by a high accuracy multidomain temporal-spatial pseudospectral method. The enclosure is filled with Boussinesq fluid and is bounded by four finite thickness and conductive walls; one of the vertical sidewall is exposed to time-periodic temperature environment while the opposite sidewall holds constant temperature; the top and bottom walls are assumed to be adiabatic. Particular efforts are focused on the effects of three types of influential factors: the wall thermophysical properties, the time-periodic temperature patterns and the inclination, and the time-periodic flow patterns and heat transfer characteristics are presented. Numerical results reveal that within the present parameter range, the heat transfer rate increases almost linearly with the thermal conductivity ratio and thermal diffusivity ratio but decreases with the inclination angle. Moreover, the heat transfer could be enhanced or weakened by selecting different temperature pulsating period in the case of finite thickness wall, while it is always enhanced if the walls are zero thickness. The back heat transfer and heat transfer resonance phenomena are observed, and their relationships with the time-periodic flow patterns and temperature distributions are analyzed. The findings are helpful to the understandings of the fluid flow and heat transfer mechanisms in the related enclosure configurations, and may be of engineering use in thermal design improvement.     

Flow boiling heat transfer characteristics of R123 and R134a in a micro-channel

Flow boiling heat transfer in a single circular micro-channel of 0.19 mm ID has been experimentally investigated with R123 and R134a for various experimental conditions: heat fluxes (10, 15, 20 kW/m²), mass velocities (314, 392, 470 kg/m² s), vapor qualities (0.2–0.85) and different saturation pressures (158, 208 kPa for R123; 900, 1100 kPa for R134a). The heat transfer trends between R123 and R134a are clearly distinguished. Whether nucleate boiling is suppressed at low vapor quality or not determines the heat transfer trend and mechanism in the flow boiling of micro-channels. High convective heat transfer coefficients in the two-phase flow of micro-channels enables nucleate boiling to be suppressed even at low vapor quality, depending on the wall superheat requirement for nucleate boiling. In the case of early suppression of nucleate boiling, specifically R123, heat transfer is dominated by evaporation of thin liquid films around elongated bubbles. In the contrary case, namely R134a, nucleate boiling is dominant heat transfer mechanism until its suppression at high vapor quality and then two-phase forced convection heat transfer becomes dominant. It is similar to the heat transfer characteristic of macro-channels except the enhancement of nucleate boiling and the short forced convection region.     

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow

The mixing and flowfield of a complex geometry, similar to a rearward-facing step flow but with injection, is studied. A subsonic top-stream is expanded over a perforated ramp at an angle of 30°, through which a secondary stream is injected. The mass flux of the second stream is chosen to be insufficient to provide the entrainment requirements of the shear layer, which, as a consequence, attaches to the lower guidewall. Part of the flow is directed upstream forming a re-entrant jet within the recirculation zone that enhances mixing and flameholding. A control-volume model of the flow is found to be in good agreement with the variation of the overall pressure coefficient of the device with variable mass injection. The flowfield response to changing levels of heat release is also quantified. While increased heat release acts somewhat analogously to increased mass injection, fundamental differences in the flow behaviour are observed. The hypergolic hydrogen-fluorine chemical reaction employed allows the level of molecular mixing in the flow to be inferred. The amount of mixing is found to be higher in the expansion-ramp geometry than in classical free-shear layers. As in free-shear layers, the level of mixing is found to decrease with increasing top-stream velocity. Results for a similar configuration with supersonic flow in the top stream are reported in Part II of this two-part series.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part II: Supersonic Flow

Fundamental aspects of mixing between two gaseous streams in a complex geometry are studied and discussed. In the present paper, a supersonic top-stream is expanded over a 30° ramp, through which a secondary lower-stream is injected. The mass flux through the secondary stream is purposely insufficient to provide the entrainment requirements of the resulting shear layer, causing it to attach to the lower guidewall. Part of the shear layer fluid is directed upstream forming a recirculation zone, with enhanced mixing characteristics. The pressure coefficient of the device is quantified as a function of velocity ratio. The effect of heat release on the pressure coefficient is also reported. Molecular mixing was measured employing “flip” experiments based on the hypergolic hydrogen-fluorine chemical reaction. The amount of mixing for the expansion-ramp geometry is found to be higher than in classical free shear layers. However, as in free shear layers, the level of mixing decreases with increasing top-stream velocity. Results for a similar configuration with subsonic/transonic flow in the top stream are reported in Part I of this two-part series.     

Density and temperature ahead of a cylinder with a thermally insulated wall and a cooled wall in a rarefied hypersonic system

Results are presented of a measurement of density and temperature on the stagnation line of a cylinder in cross flow at Mach number M_∞=5, Knudsen number Kn_∞=0.06?0.33, and with temperature factor varying from 1 to 0.11. The effect of degree of rarefaction and the temperature factor on the structure of the perturbed region ahead of the cylinder has been investigated.     

Flow behavior in microchannel made of different materials with wall slip velocity and electro-viscous effects

In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressuredriven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the fow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large kh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.     

Nonlinear evolution analysis and stability for convection in a mushy layer with permeable interface

We consider the problem of two- and three-dimensional nonlinear buoyant flows in horizontal mushy layers during the solidification of binary alloys. We study the nonlinear evolution of such flow based on a recently developed realistic model for the mushy layer with permeable interface. The evolution approach is based on a Landau type equation for the amplitude of the secondary nonlinear solution, which can be in the form of rolls, squares, rectangles or hexagons. Using both analytical and computational methods, we calculate the solutions to the evolution equation near the onset of motion for both subcritical and supercritical regimes and determine the stable solutions. We find, in particular, that for several investigated cases with different parameter regimes, secondary solution in the form of subcritical down-hexagons or supercritical up-hexagons can be stable. However, the preferred solution for smallest values of the Rayleigh number and the amplitude of motion is in the form of subcritical down-hexagons. This result appears to agree with the experimental observation on the form of the convective flow near the onset of motion.     

Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side

We study both experimentally and numerically the convective flow in a tall vertical slot with differently heated walls. The flow is investigated for the fluid with the Prandtl number Pr=26, which is large enough to ensure the traveling waves as primary instability and small enough to prevent boundary layer convection. The flow evolution is determined on the base of the visual observations, power spectra and amplitude analysis. In the numerical simulations of two- and three-dimensional flows, we accept an assumption of an infinite fluid layer. The satisfactory agreement with experiment is observed, and the sequence of convection states is discovered. It starts with a plane-parallel flow as primary solution, which becomes unstable to two counter-propagating waves. It is followed by a tertiary three-dimensional flow in the form of wavy traveling waves. As the Grashof number is increased even further, a chaotically oscillating cellular pattern consisting of the pieces of broken waves arises. The formation of a structure in the form of the vertical rolls chaotically modulated along axes concludes this complicated picture.     

A visual study on complex flow structures and flow breakdown in a boundary layer transition

A visualization study is conducted on the excited laminar-turbulent transition within a flat plate boundary layer flow in a water tunnel. The hydrogen bubble technique is employed to investigate the complex characteristics of the flow structure and its breakdown in the later stages of the transition. A new flow structure is observed, which involves two secondary hairpin vortices outboard of both legs of a primary hairpin vortex. This complex structure is argued to be a precursor of a turbulent spot in this K-type transition. Also reported in the paper is the evolution of the flow structure and its subsequent breakdown, manifested by the emergence of dark spots, low-speed fluid bumps, and near-wall hairpin vortex groups. The results indicate that the near-wall flow breakdown is the result of instability of a local three-dimensional high-shear layer between the low-speed fluid bump and the outer higher-speed region.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low Reynolds numbers

Numerical simulation and flow visualization were performed to study the dynamical behavior of vortices generated in channels with two different geometries, i.e., a periodically converging–diverging channel and serpentine channel, both having sinusoidal wavy walls. This system for pulsatile flow is used to enhance heat and mass transfer in very viscous liquids. The numerical results predict well the dynamical behavior of vortices and agree with the flow visualizations. For both channels, the vortex expands in each furrow of the channel walls during the deceleration phase and shrinks during the acceleration phase, which leads to fluid exchange between the vortex and the mainstream. The time-averaged vortex strength and wall shear stresses increase, as the frequency of fluid oscillation increases under a fixed oscillatory fraction of the flow rate. However, above a certain value of the frequency, they reversely decrease due to viscous effects. This frequency for the serpentine channel is smaller than that for the converging–diverging channel. The channel geometries are found to have an important effect of the flow characteristics.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.     

Steady mixed convection boundary layer flow over a vertical flat plate in a porous medium filled with water at 4°C: case of variable wall temperature

The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated with water at 4°C (maximum density) when the temperature of the plate varies as x ^m and the velocity outside boundary layer varies as x ^{2 m} , where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel to a free stream velocity U _∞ oriented in the upward or downward direction, while the ambient temperature is T _∞ = T _m (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme. Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles are obtained and discussed for different values of the mixed convection parameter λ and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible for large values of λ and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of λ and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at 4°C (maximum density) compared to water at normal temperature.